Calculus: How to Do Math

Maths the Queen of Sciences

05/29/2011

~ Oscar4

I really wish to congratulate the maker of these series. He is a great teacher, funny and rigorous. He knows the subject very well and his presentation skills are brilliant.

Oscar Lima
Mathematics Teacher
29 May 2011,Sydney, Australia.

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The Basics
Overview
How to do Math Page [1 of 1]
How to do mathematics. Yeah, this is a great question, and I love talking about this because I think a lot of people don't know how to do mathematics. And it's a great thing to actually figure out, especially early on in a course, especially in your calculus class. You know, people think well, gee, the way I study mathematics is, I'll take really careful notes, I'll really listen to the professor, if there is a teacher assistant, I'll go to all the TA sessions, and write everything down, and then I'll do all the homework. And afterwards, when I'm preparing for the exam, I'll look through my notes and read them very carefully and make an outline up, take real careful look at the notes, look over my old homework, see if there are any mistakes, and therefore I'll be really prepared. No, no, no, no, no, no, no, no, no, no. That's not the way to do mathematics. The way to do mathematics is to just that. Do mathematics. Reading over notes, looking at old problems, bla, bla, bla, bla, bla, bla. Math is not a spectator sport, you really should think about mathematics as playing some sort of game.
Suppose you want to learn how to play tennis. Okay, there are a number of ways you can learn how to play tennis. Here is one approach. What you can do is get about fifteen hours of John McEnroe playing tennis, you know, amazing tennis player. And you have video tapes of him in various matches playing various games and what not, and you sit down earnestly in your room and, you know, you have some chips and stuff, but you really concentrate, and you watch these fifteen hours of video and really intensely. I mean not just goofing off, you're really watching because you want to learn to play tennis. After those fifteen hours, you come out and you say, okay, well now I know how to play, I've watched this expert and he makes it look so easy, and you get out on the court, you don't even know how to hold the tennis racket.
See, this is exactly what mathematics is like. If you want to learn how to play tennis, what you've got to do, is you've got to play tennis. You've got to learn how to hold the racket. You've got to learn how to throw the ball. You've got to learn how to hit. You've got to learn your backhand. You've got to learn how to run around. You've got to learn how to read the opponent. This is what mathematics is. You've got to do it. Reading about it, hearing someone else talk about it, even me, as wonderful as I am, it's not going to do it for you. You have got to do it, and the way you do it is by actively trying examples and problems, and working through things, and that's the way you are going to know if you really have conquered the subject.
So what you've got to do, if you want to do mathematics, is literally just that. Do it. So, when there are homework assignments, of course you do those. You go to lectures. You learn about the ideas. You tried to make it your own, but then after all that, when it's time to prepare for an exam, or for a quiz, or just to see if you are on the ball on things, you must do problems. Do lots of examples; work them out and if you run out of examples, you know what you do? You go to either here where we have some examples, and when you use those, go to the library and check out another calculus book. There's tons of them there, and they are big and fat, and they got thousand's of problems in there. The answer is in the back of the book, you can check the answers, but be careful, many, many, many times the answers in the back of the book are wrong. Well, they hire some people to find the answers in the back of the book, and those people are great. But yeah, mistakes are made, and in fact, when they print them up, there are typographical errors and what not, and I have seen so many calculus students come in to my office and say Professor Burger, I tried to work number 17 down, I got this answer and the back of the book says this. And I look at there work, it's absolutely perfect, they did the problem perfectly correct, turns out there was a typo in the back of the book on number 17. Well, the back of the book should not be treated as sort of a Shroud of Turin, or something, or some sort of religious or philosophic significance, it's the back of the book, okay? Not a big deal. Ideally, I would love it, I sincerely would love it if you would come to a point where you are so confident in what you are doing, and feel so secure in the mathematics that you are producing, that you produce an answer, you look in the back of the book, and just very casually and confidently state, "The book is wrong." That is a great thing to shoot for, in fact, if you can do that.
Anyway, the point is to do a lot of examples and get feed back and look at it. When preparing for a test by the way, that's exactly what you should be doing. Looking over notes is reasonably important to get a sense of where things are. Maybe you forgot exactly the details of the chain rule, looking back here, we talked about that kind of thing, but really, at the end of the day, what you've got to be doing is working through a lot of examples, and working them through on your own, and don't redo old problems too much, or if you want to a little, that's fine. But the truth really is, on the test, no one's going to ask you to do a problem, you've already done. It's extremely rare, in fact, the problems, will be new and fresh. The more you do, the more variety you see, the better prepared you are to tackle those basic issues. So, bottom line, do math, do math. Okay, now back to math, see you there.